Movement-Assisted Sensor Deployment
Guiling Wang, Guohong Cao, and Tom La Porta Department of Computer Science & Engineering
The Pennsylvania State University Email:fguiwang,gcao,[email protected]
Abstract— Sensor deployment is an important issue in
de-signing sensor networks. In this paper, we design and eval-uate distributed self-deployment protocols for mobile sen-sors. After discovering a coverage hole, the proposed pro-tocols calculate the target positions of the sensors where they should move. We use Voronoi diagrams to discover the cov-erage holes and design three movement-assisted sensor de-ployment protocols, VEC (VECtor-based), VOR (VORonoi-based), and Minimax based on the principle of moving sen-sors from densely deployed areas to sparsely deployed areas. Simulation results show that our protocols can provide high coverage within a short deploying time and limited move-ment.
Index Terms: Sensor deployment, simulations, mobile sensor, Voronoi diagram.
I. INTRODUCTION
Wireless sensor networks are expected to be intensively utilized in the future since they can greatly enhance our ca-pability of monitoring and controlling the physical environ-ment. Sensor networks are revolutionizing the traditional methods of data collection, bridging the gap between the physical world and the virtual information world [1], [2], [3], [4]. Due to the inextricable relation with the physical world, the proper deployment of sensors is very important for the successful completion of the sensing tasks issued [5], [6], [7].
Sensor deployment has received considerable attention recently. Most of these work [5], [8], [9], [10] assume that the environment is sufficiently known and under con-trol. However, when the environment is unknown or hostile such as remote harsh fields, disaster areas and toxic urban regions, sensor deployment cannot be performed manually. To scatter sensors by aircraft is one possible solution. How-ever, using this technique, the actual landing position can-not be controlled due to the existence of wind and obstacles such as trees and buildings. Consequently, the coverage may be inferior to the application requirements no matter how many sensors are dropped. Moreover, in many cases, such as during in-building toxic-leaks detection [11], [12], chemical sensors must be placed inside a building from the entrance of the building. In such cases, it is necessary to
make use of mobile sensors, which can move to the correct places to provide the required coverage.
There have been some research efforts on deploying mo-bile sensors, but most of them are based on centralized ap-proaches. For example, the work in [13] assumes that a powerful cluster head is available to collect the sensor lo-cation and determine the target lolo-cation of the mobile sen-sors. However, in many sensor deployment environments such as disaster recoveries and battle fields, a central server may not be available and it is hard to organize sensors into clusters due to network partitions. Further, the cen-tralized approach suffers from the problem of single point failure. Sensor deployment has also been addressed in the field of robotics [11], [12], where sensors are deployed one by one, utilizing the location information of previously de-ployed sensors. This method is not scalable in terms of deployment time and has strong assumptions on the initial placement to guarantee the communication between the de-ployed and undede-ployed sensors. In case of network parti-tions, this method may not be feasible.
In this paper, we design and evaluate three distributed self-deployment protocols for sensor networks to address the limitations of previous work. Our problem statement is: given the target area, how to maximize the sensor coverage with less time, movement distance and message complex-ity. Given an area to be monitored, our distributed self-deployment protocols first discover the existence of cover-age holes (the area not covered by any sensor) in the target area based on the sensing service required by the applica-tion. After discovering a coverage hole, the proposed pro-tocols calculate the target positions of these sensors, where they should move. We use Voronoi diagrams to discover the coverage holes and design three movement-assisted sensor deployment protocols, VEC (VECtor-based), VOR (VORonoi-based), and Minimax based on the principle of moving sensors from densely deployed areas to sparsely deployed areas. By intensive simulations, we evaluate our protocols from various aspects: coverage, deployment time, moving distance, scalability to initial deployment and communication range, etc, and show that our protocols are very effective in terms of coverage, deployment time, and
moving distance.
The rest of the paper is organized as follows. Section II introduces the basic knowledge about Voronoi diagram. In section III, we present three self-deployment protocols. Section IV evaluates the performance of the proposed pro-tocols. Based on the simulation results, we justify our de-sign and discuss future work in Section V.
II. TECHNICALPRELIMINARY: VORONOI DIAGRAM
0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
(a) Voronoi diagram
O B C E A D V3 V5 V2 V1 V4 G (b) Voronoi polygonG p (O)of pointO
Fig. 1. Voronoi diagram
The Voronoi diagram [14], [15] is an important data structure in computational geometry. It represents the proximity information about a set of geometric nodes. The Voronoi diagram of a collection of nodes partitions the space into polygons. Every point in a given poly-gon is closer to the node in this polypoly-gon than to any other node. Fig. 1(a) is an example of the Voronoi di-agram, and Fig. 1(b) is an example of a Voronoi poly-gon. We define the Voronoi polygon of O as G
p (O) = (V p (O);E p (O)), whereV p
(O) is the set of Voronoi ver-tices of O, and E
p
(O) is the set of Voronoi edges. As shown in Fig. 1(b), V p (O) = fV 1 ;V 2 ;V 3 ;V 4 ;V 5 g, E p (O) = fV 1 V 2 ;V 2 V 3 ;V 3 V 4 ;V 4 V 5 ;V 5 V 1 g, N(O) = fA;B;C ;D;Eg, whereN(O)denotes the set of Voronoi neighbors ofO. The Voronoi edges of O are the vertical bisectors of the line passing O and its Voronoi neighbors, e.g., V
5 V
1 is
OA’s bisector. All the points inside G p
(O) are closer toOthan to any other nodes.
Our sensor deployment protocols are based on Voronoi diagrams. As shown in Fig. 1, each sensor, represented by a number, is enclosed by a Voronoi polygon. These poly-gons together cover the target field. The points inside one polygon are closer to the sensor inside this polygon than the sensors positioned elsewhere. Thus, if this sensor can-not detect the expected phenomenon, no other sensor can detect it, and then each sensor is responsible for the sens-ing task in its Voronoi polygon. In this way, each sensor can examine the coverage hole locally, and only needs to monitor a small area around it. To construct the Voronoi polygon, each sensor only needs to know the existence of its Voronoi neighbors, which reduces the communication complexity.
III. MOVEMENT-ASSISTED SENSORDEPLOYMENT
PROTOCOLS
Our sensor deployment protocol runs iteratively until it terminates or reaches the specified maximum round. In each round, sensors first broadcast their locations and construct their local Voronoi polygons based on the re-ceived neighbor information. Then, they examine the Voronoi polygons to determine the existence of coverage holes. If any coverage hole exists, sensors decide where to move to eliminate or reduce the size of the coverage hole. To achieve this goal, we propose three algorithms: VEC (VECtor-based), VOR (VORonoi-based) and Mini-max, based on the principle that evenly distributed sen-sors can provide better coverage. For these three proto-cols, VEC pushes sensors away from a densely covered area, VORpulls sensors to the sparsely covered area, and Minimax moves sensors to their local center area.
A. The VECtor-based Algorithm(VEC)
VEC is motivated by the attributes of electro-magnetic particles: when two electro-magnetic particles are too close to each other, an expelling force pushes them apart. As-sumed(s
i ;s
j
)is the distance between sensors
iand sensor s
j. d
aveis the average distance between two sensors when the sensors are evenly distributed in the target area, which can be calculated beforehand since the target area and the number of sensors to be deployed are known. The virtual force between two sensorss
iand s
jwill push them to move (d ave d(s i ;s j
))=2 away from each other. In case one sensor covers its Voronoi polygon completely and should not move, the other sensor will be pushedd
ave d(s i ;s j ) away. In summary, the virtual force will push the sensors d
aveaway from each other. The virtual force exerted by s j ons iis denoted as ~ F
ij, with the direction from s
jto s
0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
(a) Round 0 (b) Round 1 (c) Round 2
Fig. 2. Snapshot of the execution of VEC
Notations: N(s i ),G p (s i ), ~ F ij, ~ F b: defined before c i: whether G p (s i )is completely covered ~ v i: moving vector of s i
(1)Upon entering Discovery phase:
(1.1) settimerto bediscovery interval
enterMoving phaseupon timeout (1.2) broadcasthelloafter a random time slot
(2)Upon entering Moving phase:
(2.1) settimerto bemoving interval,
enterDiscovery phaseupon timeout (2.2) ifc
i
=falsethen
callVEC()=call VOR and Minimax
in other protocols=
(2.3) Done when satisfying stop criteria (3)Upon receivinghellomessage from sensors
j: (3.1) UpdateN(s i )andG p (s i ) (3.2) ifG p (s i
)is newly covered then
setc i
=true
BroadcastOK=only forVEC= =The following is only forVEC,
and will be replaced in VOR and Minimax=
(4)Upon receivingOKmessage from sensors j: (4.1) setc j= true (5)VEC() (5.1)v~ i = ~ 0 (5.2) for eachs jin N(s i ) if(c j 6=true)^(d ave >d(s i ;s j ))then j ~ F ij j=(d ave d(s i ;s j ))=2;v~ i =v~ i + ~ F ij if(c j =true)^(d ave >d(s i ;s j ))then j ~ F ij j=d ave d(s i ;s j );v~ i =v~ i + ~ F ij (5.3) if(d ave =2>d b (s i ))then j ~ F b j=d ave =2 d b (s i );v~ i =v~ i + ~ F b (5.4) domovement adjustment
Fig. 3. The VEC protocol at sensors i
In addition to the virtual forces generated by sensors, the field boundary also exert forces, denoted as~
F
b, to push sen-sors too close to the boundary inside. ~
F bexerted on s iwill push it to moved ave =2 d b (s i ), whered b (s i )is the distance ofs
ito the boundary. Since d
aveis the average distance be-tween sensors,d
ave
=2is the distance from the boundary to the sensors closest to it when sensors are evenly distributed. The final overall force on sensors is the vector summa-tion of virtual forces from the boundary and all Voronoi neighbors. These virtual forces will push sensors from the densely covered area to the sparsely covered area. Thus, VEC is a “proactive” algorithm, which tries to relocate sen-sors to be evenly distributed.
As an enhancement, we add a movement-adjustment scheme to reduce the error of virtual-force. When a sen-sor determines its target location, it checks whether the lo-cal coverage will be increased by its movement. The lolo-cal coverage is defined as the coverage of the local Voronoi polygon. If the local coverage is not increased, the sensor should not move to the target location. Although the gen-eral direction of the movement is correct, the local cover-age may not be increased because the target location is too far away. To address this problem, the sensor will choose the midpoint between its target location and its current lo-cation as its new target lolo-cation. If the local coverage is increased at the new target location, the sensor will move; otherwise, it will stay.
Fig. 2 shows how VEC works. Round 0 is the initial random deployment of 35 sensors in a 50m by 50m flat space, with the sensing range of6meters. The initial cov-erage is75:7%. After Round 1 and Round 2, the coverage is improved to92:2% and 94:7% respectively. A formal description of the VEC algorithm is shown in Fig. 3.
B. The VORonoi-based Algorithm (VOR)
Compared to the VEC algorithm, VOR is apull-based algorithm which pulls sensors to their local maximum
cov-0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
(a) Round 0 (b) Round 1 (c) Round 2
Fig. 4. Snapshot of the execution of VOR
Si B A Fig. 5. VOR Sj A Si
Fig. 6. Inaccurate Voronoi polygon
erage holes. In VOR, if a sensor detects the existence of coverage holes, it will move toward its farthest Voronoi ver-tex (denoted asV
far). Fig. 5 shows how VOR works. The solid polygon isG
p (s
i
). The small white circles represent s
i’s Voronoi neighbors and the large circle represents the sensing circle. PointAis the farthest Voronoi vertex ofs
i and d(A;s
i
) is longer than the sensing range. Sensor s i moves along lines
i
Ato Point B, whered(A;B)is equal to thesensing range.
We limit the maximum moving distance to be at most half of the communication range to avoid the situation shown in Fig. 6, where s
i is not aware of the existence ofs
j because of communication limitations, and its local view of G
p (s
i
) (shown in the dotted line) is not correct (shown in the solid line). Otherwise, if s
i moves toward point A and stops at a distanced(A;B)(sensing range),s
i has moved more than needed.
VOR is a greedy algorithm which tries to fix the largest hole. Moving oscillations may occur if new holes are gen-erated due to sensor’s leaving. To deal with this problem, we addoscillation control which does not allow sensors to move backward immediately. Each time a sensor wants to move, it first checks whether its moving direction is oppo-site to that in the previous round. If yes, it stops for one round. In addition, the movement adjustment mentioned in VEC is also applied here.
The deployment protocol using VOR is similar to the VEC Protocol, except that in line (2.2)VEC()is replaced byVOR (), which is shown below.
Notations:
d
max: maximum moving distance ~
v
i;f: vector from s ito V far VOR () (1)v~ i =~v
i;f - sensing range
(2) shrinkjv~ i jto bed maxif j~v i j>d max (3) dooscillation control (4) domovement-adjustment
Fig. 4 shows of how VOR works. With the original coverage75:7%, after round 1 and round 2, the coverage is improved to89:2%and95:6%respectively.
C. The Minimax Algorithm
Similar to VOR, Minimax fixes holes by moving closer to the farthest Voronoi vertex, but it does not move as far as VOR to avoid the situation that the vertex which was originally close becomes a new farthest vertex. Minimax chooses the target location as the point inside the Voronoi polygon whose distance to the farthest Voronoi vertex is minimized. We call this point theMinimax point, denoted asO
m. This algorithm is based on the belief that a sensor should not be too far away from any of its Voronoi ver-tices when the sensors are evenly distributed. Minimax can
reduce the variance of the distances to the Voronoi Ver-tices, resulting in a more regular shaped Voronoi polygon, which better utilizes sensor’s sensing circle. Compared with VOR, Minimax considers more information and it is more conservative. Compared with VEC, Minimax is “re-active”; it fixes the hole more directly by moving toward the farthest Voronoi vertex.
The following terms are used to calculate the Minimax point. A circle centered at pointOwith radiusris denoted C(O;r). The circumcircle of three points V
u, V v, V w is denoted asC(V u ;V v ;V w
). Specifically, we define the Min-imax circleC m (O m ;r m )as follows:
Definition 1: Minimax circleC
m (O m ;r m )is the circle centered at the Minimax point O
m, with radius r m = d(O m ;V far ).
The Minimax circle must pass at least two Voronoi ver-tices, which is proved as the following,
* d V δ m ^ O m O far V
Fig. 7. Proof of Lemma 1
Lemma 1: C m (O m ;r m
)must pass at least two Voronoi vertices.
Proof: (by contradiction) By definition,C
m (O m ;r m ) must passV far. Suppose C m (O m ;r m
)does not pass any other vertices. Let
d =max V2V p ;V6=V far fd(O m ;V)g: (1) Thend <r m =d(O m ;V far ). LetÆ =(r m d )=2and ^ O
mbe the point on line O m V farsuch that d(O m ; ^ O m )=Æ (shown in Fig. 7). Then,
d( ^ O m ;V far )=r m Æ<r m : (2)
Based ontriangle inequality, we have
d( ^ O m ;V)d( ^ O m ;O m )+d(O m ;V)=Æ+d(O m ;V); (8V 2V p ^V 6=V far ) (3) With (1) and (3), we get
d( ^ O m ;V)Æ+d =r m =2+d =2<r m ; (8V 2V p ^V 6=V far ) (4)
With (2) and (4), we get
max V2V p fd( ^ O m ;V)g<r m ; (5)
which contradicts with the assumption thatO
m is the min-imax point.
Definition 2: The circumcircle of two point V
u and V w (C(V u ;V w
)) is defined as the circle whose center is the mid-point ofV
uand V
wand whose radius is d(V u ;V w )=2. V δ Om ^ Vw Vfar Vu Vfar ( ) ( ) d* A Om
Fig. 8. Proof of Lemma 2
Lemma 2: If C m (O m ;r m
) passes exactly two Voronoi vertices: V u and V w, then C m (O m ;r m ) = C(V u ;V w ). In other words, if the Minimax circle passes only two Voronoi vertices, it must be centered at the midpoint of these two vertices.
Proof: (by contradiction) Suppose C
m (O m ;r m ) 6= C(V u ;V w ), which means C
m is not the mid-point of V u andV w. Let d =max V2V p ;V6=V far fd(O m ;V)g; (6) and letÆ = (r m d
)=2. SupposeAis the mid-point of V
u and V
w (shown in Fig. 8). Let ^ O m be the point on O m A such that d( ^ O m ;O m ) = Æ. Since 6 O m ^ O m V u = 6 O m ^ O m V w > 6 O m AV u = 6 O m AV w ==2, ( d( ^ O m ;V u )<d(O m ;V u )=r m : d( ^ O m ;V w )<d(O m ;V w )=r m : (7)
Withtriangle inequality, we have
d( ^ O m ;V)d( ^ O m ;O m )+d(O m ;V)=Æ+d(O m ;V); (8V 2V p ^V 6=V far ) (8) With (6) and (8), we get
d( ^ O m ;V)Æ+d =r m =2+d =2<r m ; (8V 2V p ^V 6=V far ) (9) With (7) and (9), we get
max V2Vp fd( ^ O m ;V)g<r m ; (10)
which contradicts with the assumption thatO
mis the min-imax point.
If the Minimax circle passes more than two Voronoi ver-tices, it is the circumcircle of these vertices. To find the Minimax point, we only need to find all the circumcircles of any two and any three Voronoi vertices. Among those circles, the one with the minimum radius covering all the vertices is the Minimax circle. The center of this circle is the Minimax point. We formally state this claim and prove it in the following: Theorem 1: Let = fC(V u ;V v ) j C(V u ;V v ) covers all vertices in V p, and V u ;V v 2 V p g S fC(V u ;V v ;V w ) j C(V u ;V v ;V w
) covers all vertices inV p, and V u ;V v ;V w 2 V p g, thenC m (O m ;r m )2 and8C(O;r)2 ;rr m. Proof: By Lemma 1,C m (O m ;r m
)passes at least two Voronoi vertices. Case1: C m (O m ;r m
)passes three or more Voronoi ver-tices. Then it is the circumcircle of any three vertices it passes. With the definition of ,C
m (O m ;r m )2 . Based on the definition ofC m (O m ;r m ),r m =min C(V;r)2 frg. Case2: C m (O m ;r m
) passes exactly two Voronoi ver-tices: V u and V w. Based on Lemma 2, C m (O m ;r m ) = C(V u ;V w
). With the definition of , C m (O m ;r m ) 2 . Based on the definition of C
m (O m ;r m ), r m = min C(V;r)2 frg.
Based on Theorem 1, we obtain the algorithm to calcu-late the Minimax point which is formally stated as below. The complexity of this algorithm isO(n
3
), wherenis the number of the Voronoi vertices. The computational cost is not high since a Voronoi polygon usually has only a few vertices. Minimax(): (1) Initializen=jV p j (2) foru=1,2,:::,n 2 forv=u+1,u+2,:::,n 1 forw=v+1,v+2,:::,n CalculateC(V u ;V v ;V w ) ifV is insideC(V u ;V v ;V w )8V 2V pthen Record it. (3) foru=1,2, . . . ,n 1 forv=u+1,u+2,:::,n CalculateC(V u ;V v ) ifV is insideC(V u ;V v )8V 2V pthen Record it.
(4) choose one with minimum radius and set the target location to be the center (5) domovement-adjustment
Fig. 9 shows how Minimax works. With the original coverage75:7%, after round 1 and round 2, the coverage is improved to92:7%and96:5%respectively.
D. Termination
The algorithm terminates naturally based on the movement-adjustment heuristic (explained in Section III-A), which does not allow sensors to move unless the local coverage can be increased. Based on the attributes of the Voronoi diagram, the coverage area is the summation of all Voronoi polygons. Consequently, the total coverage is the summation of the local coverage, which is bounded by 100%. Thus, sensors will stop naturally when the best cov-erage is obtained.
In some applications, the coverage requirement is not that high, and it is not efficient to move sensors to get a very small coverage increase. In this case, it may be necessary to terminate the deployment process before the maximum coverage is reached to save power and reduce the deploy-ment time. To terminate the deploydeploy-ment procedure earlier, we use a threshold , defined as the minimum increase in coverage below which a sensor will not move. With a larger , the deployment will finish earlier. When=0, sensors stop when the best coverage is obtained.
E. Optimizations
In some cases, the initial deployment of sensors may form clusters, as shown in Fig. 10, resulting in low initial coverage. In this case, sensors located inside the clusters can not move for several rounds, since their Voronoi poly-gons are well covered initially. This problem prolongs the deployment time, which is shown in Fig. 10, where some sensors are still clustered together after the sixth round. To reduce the deployment time in this situation, we propose an optimization which detects whether too many sensors are clustered in a small area. The algorithm “explodes” the cluster to scatter the sensors apart, if necessary, which works as follows. Each sensor compares its current neigh-bor number to the neighneigh-bor number it will have if sensors are evenly distributed. If a sensor finds the ratio of these two numbers is larger than a threshold, it concludes that it is inside a cluster and chooses a random position within an area centered at itself which will contain the same number of sensors as its current neighbors in the even distribution. The explosion algorithm only runs in the first round. It scatters the clustered sensors and changes the deployment to be close to random.
IV. PERFORMANCE EVALUATIONS
A. Objectives, Metrics, and Methodology
We measure the performance of the proposed protocols from two aspects: deployment quality and cost. Deploy-ment quality is measured by the sensor coverage and the
0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
(a) Round 0 (b) Round 2 (c) Round 3
Fig. 9. Snapshot of the execution of Minimax
0 10 20 30 40 50 0 10 20 30 40 50 Round 0 0 10 20 30 40 50 0 10 20 30 40 50 Round 1 0 10 20 30 40 50 0 10 20 30 40 50 Round 2 0 10 20 30 40 50 0 10 20 30 40 50 Round 3 0 10 20 30 40 50 0 10 20 30 40 50 Round 4 0 10 20 30 40 50 0 10 20 30 40 50 Round 5
Fig. 10. Working procedure (VOR)
time to reach this coverage. Deployment time is deter-mined by the number of rounds needed and the time of each round. The duration of each round is primarily de-termined by the moving speed of sensors, which is the me-chanical attribute of sensors. Thus, we only use the number of rounds to measure the deployment time. The Cost has two components. One is the sensor cost; to reach a cer-tain coverage, the proposed protocol needs fewer sensors than random deployment of static sensors. The other is the energy consumption of the deployment. Both mechanical movement and electronic communication consume energy, of which mechanical motion is the major part. Hence we
choose the moving distance as the evaluation metric. We measure the sensor coverage and moving distance under various system parameters: sensor density, field size, topology, communication range, and. With certain sens-ing range, the sensor density determines the sensor cover-age that can be reached, and the difficulty to reach it. We choose 30, 35, 40, and 45 sensors per 50m50m field as the sensor density in our simulation. We also vary the field size (50m50mto150m150m) and the number of sensors to test the protocols’ extendibility to large scenar-ios. We consider two kinds of initial deployments. One is the random distribution which can be used to model many cases such as when the sensors are dropped by an airplane from a high altitude. The other is the normal distribution, which can be used to model the case where sensors form a cluster. By varying the standard deviation, we can control the dense degree of the sensor clustering.
Communication range is another important factor since it affects the accuracy of the constructed Voronoi diagram depending on which sensors detect the coverage hole and choose the target locations. We will vary the communica-tion range from 10m to 28m to see how the performance is affected. 20mis what is used in most sensor prototypes. We choose higher communication range to quantify the performance improvement. 10mis the point at which net-work partitions become common. For example, when36 sensors are deployed in a50mby50mfield and when they are in their optimal sensing position, the minimum distance between two sensors is6
p
(2), which is about8:5m. If the communication range is less than this value, the net-work is totally disconnected when sensors are in their opti-mal sensing position.
We implemented the proposed protocols in ns2 (version 2.1b9a). The target field is chosen to be 50m50m flat space except in the evaluation of our scheme’s sensitivity to the field size (in section IV-B.3). The initial placement
of sensors follows random distribution except in the evalu-ation of the impact of topology. All simulevalu-ation results are under=0except in the testing of our algorithm’s sensi-tivity to. We use 802.11 as the MAC layer protocol and DSDV as the routing protocol. The physical layer is mod-eled after the RF MOTE from Berkeley, with 916.5MHZ OOK 5kbps as the bandwidth and 20 meters as the trans-mission range except in the evaluation of the impact of communication range. Based on the information from [16], we set the sensing range to be 6 meters. This is consis-tent with other current sensor prototypes, such as Smart Dust (U.C.Berkeley), CTOS dust, Wins (Rockwell)[17], and JPL[18]. B. Simulation Results 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 20 30 40 50 60 70 80 90 coverage
The number of nodes
Fig. 11. Coverage (randomly deployed)
1) Coverage and Sensor Cost: The coverage of
ran-domly deployed sensor networks under different sensor density is shown in Fig. 11, which shows that about 85 sensors are required to reach 98% coverage. In contrast, by using our sensor deployment protocols, only 40 sensors (shown in Fig. 12(a)) are needed to reach the same cover-age.
From Fig. 12(a) and Fig. 12(b), we can see Minimax performs the best, while VEC performs the worst. Mini-max fully utilizes the local Voronoi polygon. It fixes the coverage hole directly by moving toward the largest hole, while avoiding the possible negative effect by the sensor’s movement. In addition, by locating sensors in the Mini-max point, MiniMini-max lowers the variance of a sensor’s dis-tances to its Voronoi vertices, resulting in a more regular shaped Voronoi polygon. VOR fixes the coverage hole more greedily, but lacks a comprehensive consideration. It is expectable that VOR performs worse than Minimax. One thing to be noted is in the first round, VOR is better than Minimax. This is because initially the coverage holes are normally bigger than in the middle of the deployment
0.7 0.75 0.8 0.85 0.9 0.95 1 0 2 4 6 8 10 Coverage Round VEC(n=30) VOR(n=30) Minimax(n=30) VEC(n=40) VOR(n=40) Minimax(n=40) (a) 0.75 0.8 0.85 0.9 0.95 1 0 2 4 6 8 10 Coverage Round VEC(n=35) VOR(n=35) Minimax(n=35) VEC(n=45) VOR(n=45) Minimax(n=45) (b) Fig. 12. Coverage
procedure, thus to fix them greedily can result in a higher coverage increase.
VEC performs the worst for several reasons. The pri-mary one is that VEC is sensitive to the initial deployment. Consider an extreme situation, where sensors are located in the same line with the same inter-distance. In this case, no sensor will move, since the virtual forces offset each other, though there are large coverage holes. If the sensors are lo-cated in a similar relative position initially, VEC does not perform well. In addition, VEC neither considers cover-age holes nor utilizes any geometric information from the Voronoi polygon when choosing the target location. It tries to reach a relatively balanced position among the sensors, which is very hard, for the difficulty of obtaining an exact global even distribution from only local information.
2) Moving Distance: Fig. 13 shows the average
cu-mulative moving distance after each round. From the fig-ure, we can see an interesting phenomena about VEC: the moving distance is similar under different sensor densi-ties. This is because VEC fixes coverage holes by push-ing sensors into a relatively even distribution. In VEC,
0 1 2 3 4 5 6 7 0 2 4 6 8 10 Moving distance (m) Round VEC(n=30) VOR(n=30) Minimax(n=30) VEC(n=40) VOR(n=40) Minimax(n=40) (a) 0 1 2 3 4 5 6 0 2 4 6 8 10 Moving distance (m) Round VEC(n=35) VOR(n=35) Minimax(n=35) VEC(n=45) VOR(n=45) Minimax(n=45) (b)
Fig. 13. Moving distance
sensors are pushed by the virtual forces, which are deter-mined by the difference between the average distance of sensors when they are evenly distributed and the individual inter-distances. Both values increase with a low density and decrease with a higher density. Thus, the difference is not that sensitive to the sensor density. In contrary, Mini-max and VOR relocate sensors by measuring the coverage holes, which are larger under lower density and smaller un-der high density. In addition, the curves of VEC is the flat-test among these three since the movement is very small when sensors arrive at a relatively balanced position.
Between Minimax and VOR, the former always moves a longer distance. Minimax not only tries to fix holes, but also tries to reach more regular shaped Voronoi polygons. Thus, after the first two rounds and the remaining holes are relatively small, VOR moves sensors slightly while Mini-max makes sensor move longer to the MiniMini-max points.
3) Extendibility to Large Scenarios: To test the
sensi-tivity of our methods to field size and network scale, we fix the sensor density to be40sensors per50m50mfield, and vary the field size from50m50mto150m150m. The coverage reached and the moving distance after ten rounds
is shown in Table I. From the data, we can see that our al-gorithms are extensible to large deployment scenarios, be-cause the communication and movement are kept local in our protocols. In addition, we notice that the performance is slightly better with large field size. This is because the sensing circle is better utilized inside the field than beside the boundary. With a large field, the percentage of sensors inside is higher. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 2 3 4 5 6 7 8 9 10 Coverage σ n = 30 n = 40 n = 50 n = 60 n = 70 n = 80
Fig. 14. Reference normal distribution
4) Impact of Topology: The simulation results in the
previous sections indicate that our algorithms perform quite well if the initial deployment is random. In this sec-tion, we examine the performance on other types of topolo-gies. Fig. 14 shows the coverage under different and sensor density when sensors are deployed following the normal distribution. With as high as 80sensors, the cov-erage cannot reach80%even whenis 10. By comparing this figure with Fig. 15, we can see the effectiveness of our algorithms.
Fig. 15 presents a dense clustering scenario. All 40 sen-sors are deployed around the center of the field with a nor-mal distribution. We use = 1 and = 5to represent the clustering degree of sensors. It is a very rigid situation when is equal to 1, since the initial coverage is below 10%, and about 28 sensors are located within the circle of one meter radius. The data includes both the basic version of the algorithm and the optimized version. In Fig. 15, VEC-o, VOR-o, and Minimax-o represent the optimized version.
As mentioned in SectionIII-E, our basic algorithms have difficulties in dealing with this high-degree clustering, es-pecially when = 1. In this case, VEC works bet-ter than other algorithms in the first several rounds, be-cause it pushes sensors into balanced positions aggres-sively. Though Minimax can not increase the coverage as quickly as in the random case, it can increase the cover-age steadily. It surpasses VEC after the tenth round when
50m50m 100m100m 150m150m
Coverage Moving Distance(m) Coverage Moving Distance(m) Coverage Moving Distance(m)
VEC 97:15% 4.45 97:41% 4.38 97:52% 4.33
VOR 98:50% 3.91 98:73% 3.78 98:80% 3.75
Minimax 99:17% 4.91 99:35% 4.79 99:67% 4.82
TABLE I
COVERAGE REACHED UNDER DIFFERENT FIELD SIZE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 2 4 6 8 10 Coverage Round VEC-o VOR-o Minimax-o VEC VOR Minimax (a)=1 (n=40) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 2 4 6 8 10 Coverage Round VEC-o VOR-o Minimax-o VEC VOR Minimax (b)=5 (n=40)
Fig. 15. Normal Distribution
=1, and after the seventh round when=5. This again demonstrates that Minimax has advantage in coverage.
Though our basic algorithm cannot deal well with the problem of a high degree clustering, the high coverage reached after the first round shows the effectiveness of our optimized algorithm in scattering sensors from being stick together. In addition, the explosion done in the first round does not add additional cost, instead, the deployment cost is reduced compared with the basic version. Table II presents additional data. From the number of movements and the moving efficiency, we can see that the optimized algorithm does not add additional cost while the round number and reached coverage tell us the optimized algorithm reduces
R C D (m) E M VEC-o 10 98:29% 23.00 1.24 3.43 VEC 20 84:04% 16.00 1.39 4.37 VOR-o 10 98:11% 21.75 1.17 4.22 VOR 20 46:21% 8.19 1.69 1.32 Minimax-o 10 99:15% 22.81 1.20 5.38 Minimax 20 89:11% 13.76 1.18 5.73 TABLE II
IMPROVEMENT OF THE OPTIMIZATION (=1;n=40): E
measures the effectiveness of moving, which is the ratio of actual moving distance to the distance between the initial position and the final position. M shows the average number of movements of sensors. C and D refer to the coverage and to the moving distance respectively.
R is the Round number to record these data.
the deployment time significantly.
0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 10 12 14 16 18 20 22 24 26 28 Coverage Communication range (m) VEC VOR Minimax
Fig. 16. Impact on coverage (n = 40)
5) Impact of Communication Range: We randomly
de-ploy 40 sensors in the platform and vary the transmission range from10mto28mto evaluate its impact on the per-formance. Fig. 16 and Fig. 17 show the moving distance and the coverage reached after 10 rounds under different communication range. As can be seen, when the commu-nication range is lower than12m, the performance of our algorithms is reduced. When the communication range is too low, most sensors do not know all their Voronoi neigh-bors, and the constructed Voronoi diagram is not very
ac-0 5 10 15 20 25 30 35 40 45 50 10 12 14 16 18 20 22 24 26 28 Moving distance (m) Communication range (m) VEC VOR Minimax
Fig. 17. Impact on moving distance (n = 40)
curate. Consequently, sensors may get some false coverage holes and make wrong decisions about the target location. Among these three protocols, VEC is affected the least by the low communication range in terms of both moving dis-tance and coverage, since it only utilizes the Voronoi poly-gon to determine whether to move or not, but not the target position. Sensors are only affected by the virtual force from their neighbors withind
ave, so lack of knowledge of sen-sors far away does not affect the accuracy of the calculated target location.
Fig. 16 and Fig. 17 show that when the communication range is greater than 12m, the performance is quite good. However, our trace file shows that even when the commu-nication range is26m, some constructed Voronoi diagrams are not accurate. This indicates that the heuristics used to deal with the inaccuracy of constructing Voronoi polygons are very effective.
6) Coverage increase threshold : In this section, we
evaluate how affects the performance. In Table III, the values shown in the leftmost column are the product of used by sensors for determining whether to move and the number of sensors. As can be seen, with a smaller , a higher coverage can be reached, while the deployment cost is also increased. By properly setting this threshold, we can save time and energy by trading off a very small cov-erage (less than1%in the table). From table III, we also find that, whenn>0:5%, each sensor only moves about 20%more than the direct distance from the starting point to the destination. This also means that our protocols only in-cur an approximately additional 20% movement overhead compared to the centralized approach, which may not be feasible and suffer from single point failure problem.
V. DISCUSSION ANDFUTUREWORK
This paper addressed the problem of placing sensors in a target field to maximize the sensing coverage. Based
on Voronoi diagrams, we designed three distributed proto-cols to move mobile sensors from densely deployed areas to sparsely deployed areas in an iterative way. Simulation results verified the effectiveness of our protocols and pro-vided a baseline for performance under ideal conditions. In this section, we discuss some open issues that will be addressed in the future.
A. Optimal Movement vs Communication
Our protocols require sensors to move iteratively, even-tually reaching the final destination. Other approaches can be envisioned in which the sensors move only once to their destination to minimize the sensor movement. Two such approaches are a centralized approach and an approach us-ing simulated movement. Our results show that our dis-tributed algorithms only incur an approximately additional 20% movement overhead, compared to these algorithms. However, we provide significant benefit in other dimen-sions as described below.
Although the centralized approach may minimize the sensor movement, a central server architecture may not be feasible in some applications. For example, in the battle field, sensors are responsible for detecting abnormal phe-nomena and warning soldiers nearby. No central server in the battle field can help these sensors, and an individ-ual censor does not have the computation power of a cen-ter server. In the case of an in-building toxic-leak, mobile sensors have to self deploy into the building from outside without server support. Further, the centralized approach suffers from the problem of single point failure.
Another alternative method is to let sensors stay fixed and obtain their final destinations by simulated movement. With the same round-by-round procedure, sensors calcu-late their target locations, logically move there, and ex-change these locations with the sensors which would be their neighbors as if they had actually moved. The real movement only happens at the last round when they get the final destinations. We did not deploy this alternative method for two reasons. First, an approach using simu-lated movement is susceptible to poor performance under network partitions which are likely to occur in a sensor deployment. If a network partition occurs, each partition will exercise the movement algorithms without knowledge of the others. Consequently, the obtained final destina-tion is not accurate and the required coverage cannot be reached. Using real movement, the network partitions will be healed allowing all sensors to be eventually considered in the algorithm. A second reason is the high communica-tion overhead. To guarantee logical neighbors are reached, a network-wide broadcast is needed when using simulated
n VEC VOR Minimax R C(%) D M E R C(%) D M E R C(%) D M E 0:0% 47.56 98.44 5.18 3.67 1.62 37.88 98.74 4.19 6.30 1.60 41.39 99.49 5.31 6.88 1.50 0:1% 14.23 97.87 4.57 2.55 1.47 12.00 98.57 3.62 2.74 1.47 13.71 99.11 4.28 3.67 1.35 0:5% 8.00 97.24 4.02 1.70 1.41 7.00 97.92 3.13 1.67 1.30 9.44 98.37 3.49 2.11 1.24 1% 6.22 96.62 3.62 1.26 1.33 5.10 97.19 2.85 1.26 1.23 6.78 97.84 3.11 1.60 1.21 2% 5.90 95.87 3.21 1.01 1.23 4.70 96.54 2.55 0.98 1.18 5.90 96.82 2.60 1.18 1.14 TABLE III
IMPACT OF(n=40)(R is the round number when all sensors stop; C, D, M, and E have been defined in Table II. These values are obtained
in the stopping round R)
mobility. If this network-wide broadcast is implemented by gossiping, the message complexity is at minimum 2rn
2 . Using actual mobility as in our protocols, a much lower message complexity,2rn, is enough.
B. Sensing Area
In this paper, the sensing area of each sensor is assumed to be a disk with radius 6m. This is the ideal case which provides us with a baseline of the sensor placement prob-lem. In future work, we will address varying sensing ranges and investigate such cases. Here, we discuss these issues.
Our protocols can deal well with the case of a larger or smaller sensing radius if the sensing area is uniformly a disk. The performance of the protocol depends more on the ratio of communication range to sensing range than the absolute sensing range. As the sensing range decreases with regard to the communication range, our protocols will perform very well because they can accurately construct the Voronoi diagrams. As the sensing range increases, we need to enlarge the broadcast hops to better construct the Voronoi cells.
If the sensing area is an irregular shape, instead of a disk, sensors can still check their Voronoi cells to determine the coverage holes. In this case, we can decrease the sensing range used in our protocols to account for the reduced cov-erage. In future work, we will study our protocol’s sensi-tivity to the sensing area.
C. Extend to Large Sensor Networks
In our simulation, we use a50m 50m(and 150m 150m) field and tens of sensors. In some situations, per-haps thousands of sensors are needed in a very large field. Simulation shows that the protocols presented here are not sensitive to the scale of the network and the target field; the performance of our algorithm depends on the density of sensors used in the field. This is because communication and movement are kept local.
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